Geometry & Topology
- Geom. Topol.
- Volume 21, Number 2 (2017), 1179-1230.
A very special EPW sextic and two IHS fourfolds
We show that the Hilbert scheme of two points on the Vinberg surface has a two-to-one map onto a very symmetric EPW sextic in . The fourfold is singular along planes, of which form a complete family of incident planes. This solves a problem of Morin and O’Grady and establishes that is the maximal cardinality of such a family of planes. Next, we show that this Hilbert scheme is birationally isomorphic to the Kummer-type IHS fourfold constructed by Donten-Bury and Wiśniewski [On 81 symplectic resolutions of a 4–dimensional quotient by a group of order , preprint (2014)]. We find that is also related to the Debarre–Varley abelian fourfold.
Geom. Topol., Volume 21, Number 2 (2017), 1179-1230.
Received: 28 September 2015
Revised: 28 January 2016
Accepted: 3 March 2016
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14D06: Fibrations, degenerations 14J35: $4$-folds 14J70: Hypersurfaces 14K12: Subvarieties 14M07: Low codimension problems
Secondary: 14J50: Automorphisms of surfaces and higher-dimensional varieties 14J28: $K3$ surfaces and Enriques surfaces
Donten-Bury, Maria; van Geemen, Bert; Kapustka, Grzegorz; Kapustka, Michał; Wiśniewski, Jarosław. A very special EPW sextic and two IHS fourfolds. Geom. Topol. 21 (2017), no. 2, 1179--1230. doi:10.2140/gt.2017.21.1179. https://projecteuclid.org/euclid.gt/1510859177